Modeling Inverse Covariance Matrices by Basis Expansion – Dr. Peder A. Olsen (IBM T.J. Watson Research Center)
This talk introduces a new covariance modeling technique for Gaussian Mixture Models. Specifically the inverse covariance (precision) matrix of each Gaussian is expanded in a rank-1 basis. A generalized EM algorithm is proposed to obtain maximum likelihood parameter estimates for the basis set and the corresponding expansion coefficients for the precision matrices of individual Gaussians. This model, called the Extended Maximum Likelihood Linear Transform (EMLLT) model, is extremely flexible: by varying the number of basis elements from d to d(d+1)/2 one gradually moves from a Maximum Likelihood Linear Transform (MLLT) model (also known as semi-tied covariance) to a full-covariance model. Experimental results on two speech recognition tasks show that the EMLLT model can give relative gains of up to 35% in the word error rate over a standard diagonal covariance model, 30% over a standard MLLT model.